Arnie is desperate to do the right thing by the mother of his four legitimate children, and has been paying her a ‘substantial amount’ of money to support them, according to sources.

The former California governor reportedly set up an arrangement soon after the couple split — and Maria Shriver is taking every penny, despite the fact she’s part of the Kennedy clan and super rich in her own right!

“(He’s paying) a significant amount of child support. Arnold Schwarzenegger is also paying for his sons, Patrick and Christopher‘s private school bills,” a source tells RadarOnline.

To his credit, Arnold has volunteered the payments — he’s not obliged to give Maria ANYTHING until one of them has filed for divorce, and neither party has yet.

Few would blame Maria for accepting the money — after the trauma he has put her through!

The source adds, “Even though Maria is a Kennedy, and has inherited a great deal of money from her parent’s estate since their deaths, she is taking the child support. Under California law she is entitled to the child support, once either one of them files for divorce. Maria and Arnold’s lawyers have been working on a divorce settlement but in the meantime Arnold is willingly paying the money to Maria.”

“Maria wants to get a fair divorce settlement, and move on with her life,” the source says. “She has already begun to do so. She and Arnold talk quite often, it would surprise people how gracious Maria is being about the entire situation. Maria doesn’t want the kids to suffer because of stupid decisions their father made.”

What do YOU think, HollyMoms? Should Maria take Arnie’s cash — or refuse. With her Kennedy money, surely she doesn’t NEED it!